NUMERICAL MATHEMATICS A JOURNAL OF CHINESE UNIVERSITIES Vol.20 1998 CONTENTS

No.lTheLargeTimeBehaviourResearchofFul1yDiscreteFourierPseudospectra1MethodforHigher---DimensionalDeneraIizedKuramoto--SivashinskyTypeEquations''''.............................................................................................................'..'..'XiangXinminChenAnle(1)PerturbationAnalysisfortheGenera1izedLinearLeastSquaresProblem..'..'........'..'..'LiuXinguo(ll)DecidingVariablesSetforPolynomia1Ideal..'..'................'..'..'ZhangChuanlinFengGuochen(16)lnt…     

Some graphs which have ascending subgraph decomposition

1.IntroductionIn[1],Alavietal.gavethefollowingdecompositionconjecture.Conjecture.LetGbeagraphwith("1')edges.ThentheedgesetofGcanbedecomposedintonsetsgeneratinggraphsGI,G2,'IG.suchthatIE(Gi)I=i(fori=1,2,',n)andGiisisomorphictoasubgraphofGi 1fori=1,2,'.)n--1.AgraphGthatcanbedecomposedasdescribedinConjecturewillbesaidtohaveanAscendingSubgraphDecomposition(AlsoabbreviatedasASD).ThesubgraphsGIIG2,',G.aresaidtobemembersofsuchadecomposition.Furthermore,ifeachGiisastar(matching,pat…     

ON INTERPOLATION OF A CERTAIN CLASS OF FUNCTIONS

I.StatementofResultsForarealaleta~ma-c(1,Ial).Lets21.WeuseG.todenotethes-dimensionalunitcube,and(:,')todenotethescalarproductofvectors:and,inH.Form(ml,',m.)EZsand^~(Al,',A.)EHwedenotel'II^=mtl...m:a.Inparticular,ifA=(A,',A),thenwewritellmJI'=IImll^.Fulthermore,forf=(TI,'.)r.)EH,letiff=lrlI ... Ir.].Letf~(n,',r.)ERswithfi20(i~1,',s),andletf(:)beasingle--valuedfunctionsuchthatf(xl,'sxit',x.)~f(xl,')xi 1,',x.),i~1,')s.Writefi=pi fi(i~1,',s),wherepi~fi~0iffi=0an…     

GENERALIZED GAUSSIAN QUADRATURE FORMULASWITH CHEBYSHEV NODES

1.IntroductionThispaperdealswiththegeneralizedGaussianquadratureformulasforChebyshevnodes(of.[2]).Throughoutthepaperweassumethatmandnarepositiveintegers.Asusually,Tn(x)andUn(x)denotethen--thChebyshevpolynomialsofthefirstkindandthesecondkind,respectively.AmonggeneralizedGaussianquadratureformulasoneofthemostimportantcasesistheweightwin(x):~(1~x')[(m ')/']~(" ')/',(1.1)where[rldenotesthelargestinteger5r.In[5]wepointedoutthatifwetakeasnodesofaquadratureformulathezerosof(1--x')Un--100(herewere…     

DISCRETIZATION OF JUMP STOCHASTIC DIFFERENTIAL EQUATIONS IN TERMS OF MULTIPLE STOCHASTIC INTEGRALS

1.IntroductionFOrthestrongdiscretizationofSDEs,anynumericalmethodwhichonlydependsonthevaluesofBrownianpathsorPoissonpathsatthepartitionnodescannotachieveanorderhigherthan0.5ingeneral[')'1'].Thereforetheevaluationofmultiplestochasticintegralsontheintervalsbetweennodesisamajorobstaclethatmustbeovercome.Someattemptshavebeenmadepreviouslyindifferentapproachestoapproximatemul-tiplestochasticintegrals.[2]suggestsanapproximationintermsofFourierGaussiancoefficientsoftheBrownianbridgeprocess.Asthel…     

THE BLOWUP OF RADIALLY SYMMETRIC SOLUTIONS FOR 2-D QUASILINEAR WAVE EQUATIONS WITH CUBIC NONLINEARITY

61.IntroductionInthispaper,weconsiderthefollowingtwodimensionalquasilinearwaveequationswiththenonlinearityofcubicform:wherex=(x1,x2),E>Oissmallenough,c'(otu,7u)=c'(otu,Oru)=l a,(otu)' a2Ofuoru a,(oru)' o(Iotul' lorul'),f(otu'Vu)=f(otu,o'u)=b,(otu)' b,(o,u)'oru b,otu(oru)' b,(oru)' O(Iotul' loruI'),a1-a2 a3/o,uo(x),ul(x)areCooradialfunctions(thatis,smoothfunctionsoflx1')andsupportedinaffeedba.llofradiusM.Moreoveruo(x)/Ooru1(x)*O.OuraimistostudythelifespanTeofsolutionsto(l.1)andthebreakdow…     

Optimal Interior and Local Error Estimates of a Recovered Gradient of Linear Elements on Nonuniform Triangulations

1.IntroductionConsideramodelellipticboundaryvalueproblemwhereflCRd,d=1,2,3,isaboundedpolyhedraldomainwithaLip8chitzboundaryfEL'(fl),aijareLipschitz-continuousfunctionsandthematrixA=(aij)issymmetricanduniformlypositivedefinitewithrespecttoxEn.Itisknownthatthefiniteelementmethodappliedto(1.1)mayproducesomesuperconvergencephenomenaeveniftheusedmeshesarenonuniform[5'8'9'1o'121.InarecentpaPer[61,aninteriorerrorestimatefortherecoveredgradientofGalerkinpiecewiselinearaPproximationshasbeenproposed…     

由非顺序主子阵和缺损广义特征对构造对称三对角矩阵

本文讨论形如A_nX=λC_nX的方程,其中A_n是一个对称三对角矩阵,C_n是一个对角矩阵.对矩阵A_n进行3×3分块,给定A_n的一个非顺序主子阵A_(r+1,r+s),给定C_n和四个向量X_1=(x_1,…,x_r)',X_3=(x_(r+s+1),…,x_n)',Y_1=(y_1,…,y_r)',Y_3=(y_(r+s+1),…,y_n)'和两个不同实数λ,μ,构造一个对称三对角矩阵A_n和两个向量X_2=(x_(r+1),…,x_(r+s))',Y_2=(y_(r+1),…,y_(r+s))',满足A_nX=λC_nX和A_nY=μC_nY,其中X=(X_1',X_2',X_3')',Y=(Y_1',Y_2',Y_3')'.本文给出问题有解的条件,解的表达式和相应算法,并给出数值算例验证算法的有效性.     

SOME ALMOST ALL RESULTS CONCERNINGTHE PJATECKII-SAPIRO PRIME NUMBERS

51.IntroductionSupposethatr>Oisafixednumberand[oldenotes,asusuaI,theintegralpartofo.LetForo1wasfirststudiedin1953byPjateckii-Sapiro[']whoprovedthat(1.1)holdsfor1相似文献   

LIMIT THEOREMS FOR INTEGRAL TYPE ESTIMATORS WITH CENSORED DATA

1.IntroductionLetXI,X2,',X.beasequenceofnonnegativeindependentrandomvariableswithcommoncontinuousdistributionfunctionF.LetYI,Y2,',YebeanothersequenceofnonnegativeindependentrandomvariableswithcommoncontinuousdistributionfunctionG,alsoindependentof{Xi}.WecanonlyobserveZi=min(Xi,K),6i~I(x.SYi).OnewaytoestimatethedistributionfunctionForthesurvivalfunctionS~1--Ffromthesample(Zi,st)(i=l,2,')n)isthroughtheproductlimitestimatordueto[1].ItisdefinedbywhereZ(i)aretheorderstatisticsofZian…     

Homotopy perturbation method for fractional KdV-Burgers equation

In the paper, we extend the homotopy perturbation method to solve nonlinear fractional partial differential equations. The time- and space-fractional KdV-Burgers equations with initial conditions are chosen to illustrate our method. As a result, we successfully obtain some available approximate solutions of them. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of nonlinear fractional partial differential equations.     

A Chebyshev spectral collocation method for solving Burgers’-type equations

In this paper, we elaborated a spectral collocation method based on differentiated Chebyshev polynomials to obtain numerical solutions for some different kinds of nonlinear partial differential equations. The problem is reduced to a system of ordinary differential equations that are solved by Runge–Kutta method of order four. Numerical results for the nonlinear evolution equations such as 1D Burgers’, KdV–Burgers’, coupled Burgers’, 2D Burgers’ and system of 2D Burgers’ equations are obtained. The numerical results are found to be in good agreement with the exact solutions. Numerical computations for a wide range of values of Reynolds’ number, show that the present method offers better accuracy in comparison with other previous methods. Moreover the method can be applied to a wide class of nonlinear partial differential equations.     

Distributed model of a self-developing market economy

Fairly rigorous mathematical laws are applied to construct a mathematical model of a self-developing market economy with movement of time-dependent capital in the technology space. The model is a system of nonlinear partial differential equations. We analyze the bifurcations of the spatially homogeneous solutions that describe the dynamics of macro-variables of the economic system. We also study some properties of the solutions of the partial differential equations that follow from diffusion of capital and consumer demand.Translated from Nelineinaya Dinamika i Upravlenie, No. 2, pp. 243–262, 2002.     

Exact solutions of some systems of fractional differential‐difference equations

In this paper, the ‐expansion method is proposed to establish hyperbolic and trigonometric function solutions for fractional differential‐difference equations with the modified Riemann–Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential‐difference equation into its differential‐difference equation of integer order. We obtain the hyperbolic and periodic function solutions of the nonlinear time‐fractional Toda lattice equations and relativistic Toda lattice system. The proposed method is more effective and powerful for obtaining exact solutions for nonlinear fractional differential–difference equations and systems. Copyright © 2014 John Wiley & Sons, Ltd.     

On abstract degenerate neutral differential equations

We introduce a new abstract model of functional differential equations, which we call abstract degenerate neutral differential equations, and we study the existence of strict solutions. The class of problems and the technical approach introduced in this paper allow us to generalize and extend recent results on abstract neutral differential equations. Some examples on nonlinear partial neutral differential equations are presented.     

Rational Jacobi elliptic solutions for nonlinear differential–difference lattice equations

In this work, we present a direct new method for constructing the rational Jacobi elliptic solutions for nonlinear differential–difference equations, which may be called the rational Jacobi elliptic function method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential–difference equations in mathematical physics via the lattice equation. The proposed method is more effective and powerful for obtaining the exact solutions for nonlinear differential–difference equations.     

Application of one constructive method for the construction of non-Lie solutions of nonlinear evolution equations

We propose a constructive method for the construction of exact solutions of nonlinear partial differential equations. The method is based on the investigation of a fixed nonlinear partial differential equation (system of partial differential equations) together with an additional condition in the form of a linear ordinary differential equation of higher order. By using this method, we obtain new solutions for nonlinear generalizations of the Fisher equation and for some nonlinear evolution systems that describe real processes in physics, biology, and chemistry. To the blessed memory of V. I. Fushchich Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 6, pp. 814–827, June, 1997.     

Long-time behavior of an angiogenesis model with flux at the tumor boundary

This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behavior of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.     

用格子Boltzmann方法模拟非线性热传导方程

对具有非线性源项和非线性扩散项的热传导方程建立格子Boltzmann求解模型.在演化方程中增加了两个关于源项分布函数的微分算子,对演化方程实施Chapman-Enskog展开.通过对演化方程的进一步改进,恢复出具有高阶截断误差的宏观方程.对不同参数选取下的非线性热传导方程进行了数值模拟,数值解与精确解吻合得很好.该模型也可以用于同类型的其他偏微分方程的数值计算中.     

Existence and uniqueness of solutions for nonlinear impulsive partial differential equations with delay

In this paper, a system of nonlinear impulsive partial differential equations with delay is investigated by the method of upper–lower solutions. The existence-uniqueness result of this system and the comparison principle of the corresponding equations are obtained. An application is given to some model problems in ecology.